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Newton's Laws of Motion

A particle of...

Question

A particle of mass $m$ is moving with a constant acceleration $2 a$ towards another particle of mass $4 m$ as shown in figure. Mass $4 m$ is also moving with acceleration $a$ towards the particle of mass $m$ . Find the acceleration of $C O M$ of the system.

a / 5

(towards left)

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2 a / 5

(towards left)

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a / 5

(towards right)

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2 a / 5

(towards right)

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Solution

The correct option is B $2 a / 5$ (towards left)
As we know,
$a_{C O M} = \frac{m_{1} a_{1} + m_{2} a_{2}}{m_{1} + m_{2}}$
$= \frac{m (2 a) + 4 m (- a)}{m + 4 m}$
(consider rightward direction as +ve)
$\Rightarrow a_{C O M} = \frac{2 m a - 4 m a}{5 m a} = \frac{- 2 a}{5}$
Hence, acceleration of $C O M$ of the system will be $\frac{2 a}{5}$ towards left

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Newton's Laws of Motion

Standard XII Physics

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A particle of mass m is moving with a constant acceleration 2a towards another particle of mass 4m as shown in figure. Mass 4m is also moving with acceleration a towards the particle of mass m. Find the acceleration of COM of the system.

The correct option is B 2a/5 (towards left)As we know, aCOM=m1a1+m2a2m1+m2 =m(2a)+4m(−a)m+4m (consider rightward direction as +ve) ⇒aCOM=2ma−4ma5ma=−2a5 Hence, acceleration of COM of the system will be 2a5 towards left

A particle of mass $m$ is moving with a constant acceleration $2 a$ towards another particle of mass $4 m$ as shown in figure. Mass $4 m$ is also moving with acceleration $a$ towards the particle of mass $m$ . Find the acceleration of $C O M$ of the system.